By a theorem of Dobrow and Smythe, the depth of the kth node in very simple families of increasing trees (which includes, among others, binary increasing trees, recursive trees and plane ordered recursive trees) follows the same distribution as the number of edges of the form j−(j+1) with j < k. In this short note, we present a simple bijective proof of this fact, which also shows that the resu...

The Least Common Ancestor Problem can be used to solve many other algorithmic problems on trees. It is shown that an efficient and simple solution is possible.

We report the lowest frequency measurements of gamma-ray burst (GRB) 171205A with upgraded Giant Metrewave Radio Telescope (uGMRT) covering a range from 250--1450 MHz and period $4-937$ days. It is first GRB afterglow detected at 250--500 second brightest uGMRT. Even though observed for nearly 1000 days, there no evidence transition to non-relativistic regime. also analyse archival ${\it Chandr...

At the very deepest molecular level, mechanisms of life depend on operation proteins, so-called “workhorses” cell. Proteins are nanoscale machines that transform energy into useful cellular work, such as ion or nutrient transport, information processing, transformation. Behind every biological task, there is a nanometer-sized molecule whose shape and intrinsic motions, binding, sensing properti...